Dr Tewari has developed computational resources with an expansible object-oriented framework in Java for handling exact coalescent recursions and doing Monte Carlo simulations with importance sampling. We have advanced our combinatorial understanding of coalescent results, resulting in concrete improvements to coalescent algorithms. In particular, for importance sampling of coalescent probabilities, Drs. Tewari and Spouge have applied exact probability calculations within the framework to increase the effective sample size by about four with negligible costs in computation time. Dr. Spouge has also developed some coalescent results relevant to barcode sampling strategies, reported in his project on DNA barcodes (LM200883).